NF weak partition development: FocusedFVPaths.
theorem
NFChoice.DefinitionLeaves.AlphaFocusedFV.fv_subset_cab_wrex_left
{outer inner : SemanticCore.Var}
{A : SemanticCore.Class}
{p : SemanticCore.Wff}
(houter : outer ∉ A.fv)
(hinner : inner ∉ A.fv)
:
A.fv ⊆ (SemanticCore.Class.cab outer (Compiler.CompactSourceSyntax.synWrex inner A p)).fv
The class parameter remains free through cab outer (wrex inner A p).
theorem
NFChoice.DefinitionLeaves.AlphaFocusedFV.fv_subset_ccompl_cab_wrex_left
{outer inner : SemanticCore.Var}
{A : SemanticCore.Class}
{p : SemanticCore.Wff}
(houter : outer ∉ A.fv)
(hinner : inner ∉ A.fv)
:
A.fv ⊆
(Compiler.CompactSourceSyntax.synCcompl
(SemanticCore.Class.cab outer (Compiler.CompactSourceSyntax.synWrex inner A p))).fv
Complement preserves the preceding focused free-variable embedding.